y=sin²x+sin2x+2cos²x
=sin2x+(1+cos2x)/2 +1
=sin2x+1/2*cos2x+3/2
=√5/2(2/√5*sin2x+1/√5*cos2x)+3/2
=√5/2sin(2x+arc tan(1/2))+3/2
2x+arc tan(1/2)= 2kπ-π/2,k∈Z
解出x得函数取最小值时的x集合
2kπ-π/2≤2x+arc tan(1/2)≤2kπ+π/2,k∈Z
解出x得单增区间
2kπ+π/2≤2x+arc tan(1/2)≤2kπ+3π/2,k∈Z
解出x得单减区间